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<DIV>20 S=1.714E-09'Stefan-Boltzmann constant</DIV>
<DIV>30 DIM E(5,5)'combined emittance matrix</DIV>
<DIV>40 DATA 0,0,70,70,0,1,70,70,0,1,70,70</DIV>
<DIV>50 DATA 0.5,0.5,70,70,0.5,0.5,70,70</DIV>
<DIV>60 DATA 1,1,70,70</DIV>
<DIV>70 'above: solar absorption, IR absorption, </DIV>
<DIV>80 ' screen temp, air temp south of
screen</DIV>
<DIV>90 TAUCUM=1'initialize cumulative layer transmission fraction</DIV>
<DIV>100 FOR I=0 TO 5'find each layer's solar absorption fraction</DIV>
<DIV>110 READ ASUN(I),AIR(I),TS(I),TE(I)</DIV>
<DIV>120 TAUCUML=TAUCUM</DIV>
<DIV>130 TAUCUM=TAUCUM*(1-ASUN(I))'cumulative layer transmission</DIV>
<DIV>140 ASUN(I)=ASUN(I)*TAUCUML'absorption fraction for layer I</DIV>
<DIV>150 NEXT I</DIV>
<DIV>160 FOR I=1 TO 4'find IR emittance fraction</DIV>
<DIV>170 FOR K=I+1 TO 5'for each pair of layers</DIV>
<DIV>180 E=AIR(I)</DIV>
<DIV>190 FOR J=I+1 TO K-1</DIV>
<DIV>200 E=E*(1-AIR(J))</DIV>
<DIV>210 NEXT J</DIV>
<DIV>220 E(I,K)=E*AIR(K)</DIV>
<DIV>230 E(K,I)=E(I,K)</DIV>
<DIV>240 NEXT K</DIV>
<DIV>250 NEXT I</DIV>
<DIV>260 TA=34'ambient temp (F)</DIV>
<DIV>270 SUN=.91^2*1000/6'sun through glazing (Btu/ft^2-h)</DIV>
<DIV>280 TR=70'air heater inlet temp (F)</DIV>
<DIV>290 CFM=1.2'airflow/ft^2</DIV>
<DIV>300 C=10'relaxation damping cap</DIV>
<DIV>310 FOR I=1 TO 499'relaxation iterations</DIV>
<DIV>320 FOR L=1 TO 5'mesh layer</DIV>
<DIV>330 GA=(TE(L-1)-TS(L))/(2/3+1/CFM)'layer air gain</DIV>
<DIV>340 GR=0'initialize rad gain</DIV>
<DIV>350 FOR K=1 TO 5</DIV>
<DIV>360 GR=GR+E(K,L)*S*((TS(K)+460)^4-(TS(L)+460)^4)</DIV>
<DIV>370 NEXT K</DIV>
<DIV>380 IF L=1 THEN GFLOW=(TA-TS(1))/1 ELSE GFLOW = 0</DIV>
<DIV>390 GFLOW=GFLOW+ASUN(L)*SUN+GA+GR'heatflow into layer</DIV>
<DIV>400 TS(L)=TS(L)+GFLOW/C'new layer temp</DIV>
<DIV>410 TE(L)=TE(L-1)-GA/CFM'air temp leaving layer</DIV>
<DIV>420 NEXT L</DIV>
<DIV>430 NEXT I</DIV>
<DIV>440 PRINT"998'";</DIV>
<DIV>450 FOR L=1 TO 4</DIV>
<DIV>460 PRINT INT(TS(L)+.5);INT(TE(L)+.5);</DIV>
<DIV>470 NEXT L</DIV>
<DIV>480 PRINT INT(TS(5)+.5);INT(TE(5)+.5)</DIV>
<DIV>490 EFF=100*6*(TE(5)-TR)*CFM*60/55/1000'solar collection efficiency
(%)</DIV>
<DIV>500 LEFF=100*(1000-6*(TS(1)-TA))/1000'glazing loss-based efficiency</DIV>
<DIV>510 PRINT "999'";EFF;LEFF</DIV>
<DIV> </DIV>
<DIV>T1 air T2 air Ts1 air Ts2 air
Tb air</DIV>
<DIV> </DIV>
<DIV>73 72 109 93 154 127 156
143 160 152</DIV>
<DIV> </DIV>
<DIV>64.62651 76.43108</DIV>
<DIV> </DIV>
<DIV>This looks good to me now, with 2 layers of IR greenhouse film and</DIV>
<DIV>2 layers of 50% black greenhouse shadecloth. A single layer of R1
film</DIV>
<DIV>with 70 F air indoors and 34 F air outdoors and no radiation loss
would</DIV>
<DIV>have a collector efficiency of 100(1000-6h(70-34))/1000 = 78.4%.</DIV>
<DIV> </DIV>
<DIV>I suspect the 2 efficiencies above don't match because I approximated</DIV>
<DIV>the heat capacity of a C cfm airstream as C Btu/h-F when it's really</DIV>
<DIV>closer to 1.08C, but I'm inclined to believe the 2nd efficiency,</DIV>
<DIV>which is nicely close to an ideal 78.4% with no radiation loss.</DIV>
<DIV> </DIV>
<DIV>Here's the solar yard heat store I'm planning now:</DIV>
<DIV> </DIV>
<DIV> 12' </DIV>
<DIV>...................
partial parts list</DIV>
<DIV>. . . . . . . . . . </DIV>
<DIV>. .
. . 15 plastic 55
gallon drums</DIV>
<DIV>. .
. . 2 10'x16' pieces
of EPDM</DIV>
<DIV>. .
. . 6 tons of 2"
clean stone</DIV>
<DIV>. .
. . 16 3'x4"-D PVC
pipes </DIV>
<DIV>. . plan view . . 22.9' 2x12'x14' ft^2
wood pallets</DIV>
<DIV>. .
. . 3x12'x14' ft^2
wire mesh</DIV>
<DIV>. .
. . 2x12'x16' IR
plastic film</DIV>
<DIV>. .
. . 1x12'x16' 50%
greenhouse shadecloth</DIV>
<DIV>. .
. . 1x12'x16' weed
barrier</DIV>
<DIV>. . . . . . . . .
. 480 ft^2 R30
insulation</DIV>
<DIV>...................
Grainger 10" fan</DIV>
<DIV> </DIV>
<DIV> 12' </DIV>
<DIV>...................
.</DIV>
<DIV>.
.
/ . .</DIV>
<DIV>.
.
16'. east . <-- 2 12'x16' layers</DIV>
<DIV>.
. / .
elevation . of IR greenhouse film</DIV>
<DIV>. south
. .
.
. </DIV>
<DIV>. elevation . 13.9' ......collar
beam.... \</DIV>
<DIV>. . . . . . . . . .
. . . . . . . . . . 16' </DIV>
<DIV>.
. 8'.
.
. . \</DIV>
<DIV>.
. . 6'. heat store
. . </DIV>
<DIV>.
. .
.
. 60.</DIV>
<DIV>.......................................................</DIV>
<DIV>
|4.3'| 14' | 4.6'|</DIV>
<DIV> </DIV>
<DIV>... 70 F air would inflate the space between the 2 layers of IR</DIV>
<DIV>greenhouse film and flow through 1/2" holes on a 14” grid in </DIV>
<DIV>the inner film into 3 N-S rows of 5 plastic 55 gallon drums in </DIV>
<DIV>a 12'x14'x6'H box which support 2 3'Wx4'Hx10'L water troughs </DIV>
<DIV>surrounded by 6 tons of rocks with about 500 ft^3 (4000 gallons)</DIV>
<DIV>of water, like this:</DIV>
<DIV> </DIV>
<DIV>
south south</DIV>
<DIV>
^
^ </DIV>
<DIV>
| 12' |</DIV>
<DIV>................................. </DIV>
<DIV> i
insulation i</DIV>
<DIV>. . . . .
. . . . </DIV>
<DIV>
n
n</DIV>
<DIV>. . D D D
D D . . </DIV>
<DIV> s p p
p p s</DIV>
<DIV>. .
4'x10'x3'H . . plan view </DIV>
<DIV>
u
u </DIV>
<DIV>. . EPDM
tank . . </DIV>
<DIV> l p p
p p l </DIV>
<DIV>. . D D D
D D .
.
14'</DIV>
<DIV> a p p
p p a</DIV>
<DIV>. .
4'x10'x3'H . . east --></DIV>
<DIV>
t
t</DIV>
<DIV>. . EPDM
tank . . </DIV>
<DIV> i p p
p p i p are
3'x4" pipes to</DIV>
<DIV>. . D D D
D D . . connect the airspaces</DIV>
<DIV>
o
o above and below the drums.</DIV>
<DIV>. . . . .
. . . . </DIV>
<DIV> n
insulation n</DIV>
<DIV>................................. </DIV>
<DIV> </DIV>
<DIV>
south south</DIV>
<DIV>
^ ^
</DIV>
<DIV>
| 6' |</DIV>
<DIV>.........................................
</DIV>
<DIV>
i
insulation
8"</DIV>
<DIV>. . . . .
. . . . . . -->
down </DIV>
<DIV> n w | 4" w
|
4" w | w f</DIV>
<DIV>. .
D R U M
. . 24"</DIV>
<DIV> s i a o i
p
o i p i o</DIV>
<DIV>. .
4'x10'x3'H .
. </DIV>
<DIV> u r i f r
a
f r a r a 48"</DIV>
<DIV>. .
EPDM tank
. . </DIV>
<DIV> l e r s e
l
s e l e m</DIV>
<DIV>. .
D R U M
. . 24" 14'</DIV>
<DIV> a m g t m
l
t m l m b</DIV>
<DIV>. .
4'x10'x3'H . .
</DIV>
<DIV> t e a o e
e
o e e e o 48"</DIV>
<DIV>. .
EPDM tank
. . </DIV>
<DIV> i s p n s
t
n s t s r</DIV>
<DIV>. .
D R U M
. . 24" </DIV>
<DIV> o h | e h
|
e h | h d</DIV>
<DIV>. . . . .
. . . . . . -->
down</DIV>
<DIV>
n
insulation
8"</DIV>
<DIV>......................................... </DIV>
<DIV> 8" 4" 4" 5"
36" 4" 5" 2"</DIV>
<DIV> </DIV>
<DIV>This would have about C = 3'x12'x14'x62.33 = 31.4K Btu/F of thermal</DIV>
<DIV>capacitance. Cooling it from 140 to 70 F would release (140-70)C</DIV>
<DIV>= 2.2 million Btu, equivalent to 2.2M/130K = 17 gallons of oil.</DIV>
<DIV> </DIV>
<DIV><A
href="http://rredc.nrel.gov/solar/old_data/nsrdb/1961-1990/bluebook/data/13739.SBF">http://rredc.nrel.gov/solar/old_data/nsrdb/1961-1990/bluebook/data/13739.SBF</A></DIV>
<DIV>says 620 Btu/ft^2 of sun falls on the ground and 1000 falls on south</DIV>
<DIV>walls on an average 30.4 F January day with a 37.9 high and a 30.4</DIV>
<DIV>average daytime temp near Philadelphia. On a clear day, 890 falls</DIV>
<DIV>on the ground and 1880 falls on south walls.</DIV>
<DIV> </DIV>
<DIV>On an average day, a south wall with a 60 degree slope would receive</DIV>
<DIV>620cos60+1000sin60 = 1176 Btu/ft^2 of sun. This store could collect</DIV>
<DIV>0.8x1176x12'x16' = 180.6K Btu/day and lose 6h(70-34)12'x16'/R1 = </DIV>
<DIV>41.5K from the glazing, for a net gain of 139.1K Btu.</DIV>
<DIV> </DIV>
<DIV>Storing 139K Btu over a 6 hour January solar collection day at a rate</DIV>
<DIV>of 139.1K/6h = 23.2K Btu/h with air cooling from 140 to 70 F requires</DIV>
<DIV>about 23.2K/(140-70) = 331 cfm of airflow, which could come from </DIV>
<DIV>a 26 watt Grainger 10" fan. If the entire stone bed warms from 70 to</DIV>
<DIV>140 F, it needs a 139.1K/(140-70) = 1987 Btu/F heat capacitance, eg </DIV>
<DIV>1987/0.16 = 12.4K lb of stone, ie 12.4K/3500 = 3.5 yd^3 or 100 ft^3</DIV>
<DIV>in 2 12x100ft^3/(12'x14')/2 = 4" layers above and below the drums. </DIV>
<DIV> </DIV>
<DIV>A 12'x14'x6' tall 140 F box with 648 ft^2 of R30 surface and a 648/30</DIV>
<DIV>= 22 Btu/h-F thermal conductance would lose 24h(140-30)22 = 57K Btu</DIV>
<DIV>on an average 30 F January day near Phila, for a net gain of about</DIV>
<DIV>139.1K-57K = 82.1K, which should be plenty for hot water for showers</DIV>
<DIV>and trickle charging for cloudy days, since 5 cloudy days in a row</DIV>
<DIV>only happen 3% of the time, if cloudy days are like coin flips.</DIV>
<DIV>A yard furnace that heats a house on average days needs more glazing.
</DIV>
<DIV> </DIV>
<DIV>Dunkle and Ellul say dP = LG^2/Rhoair(21+1750Mu/(GD)) Pascals, where</DIV>
<DIV>L = 0.2032m (8/12') is the length of the bed in the flow direction.</DIV>
<DIV>If Rhoair = 1.059 kg/m^3 and V = 331cfm/12'/14' = 2 fpm (0.01 m/s)</DIV>
<DIV>and G = 1.059V = 0.011 kg/m^2-s and Mu = 1.99E-5 Pa-s at 60 C (140 F)
</DIV>
<DIV>with equivalent pebble diameter D = 23.5 mm (0.92"), then dP = </DIV>
<DIV>0.2032G^2/(1.059x0.0235)(21+1750x1.99E-5/(0.0235G)) = 0.16 Pascals,</DIV>
<DIV>ie 0.000063 "H20 :-)</DIV>
<DIV> </DIV>
<DIV>SETP equation 3.16.16 says the volumetric heat transfer coefficient</DIV>
<DIV>Hv = 650(G/D)^0.7 = 357 W/m^3K, ie 357x8/12x12x14x0.3048^3 = 1134 W/K</DIV>
<DIV>for the whole bed, ie 2148 Btu/h-F, like 2.1 car radiators. The air-</DIV>
<DIV>stone temp diff would be 15K/2148 = 6 F. The bottom layer could use</DIV>
<DIV>more stone.</DIV>
<DIV> </DIV>
<DIV>A $70 Lasko 2155A 3-speed reversible 16" window fan can move up to</DIV>
<DIV>2470 cfm with 90 watts. On a cloudy day, it could push lots of house</DIV>
<DIV>air into the bottom. At 0.1" H20, 25 Pa = 0.2032G^2/(1.059x0.0235)</DIV>
<DIV>(21+1750x1.99E-5/(0.0235G)) makes G = 0.35 = 1.059V, ie V = 0.33 m/s,</DIV>
<DIV>ie 65 fpm, ie 65x12'x14' = 10.8K cfm. At 2000 cfm, 2000/12'/14' = 12</DIV>
<DIV>fpm, ie V = 0.06 m/s, so G = 0.064 and Hv = 1311 W/K, ie 4159 W/K</DIV>
<DIV>for the whole bed, ie 7.9K Btu/h-F, like 8 car radiators.</DIV>
<DIV> </DIV>
<DIV>Nick</DIV></DIV></DIV></BODY></HTML>